Power transmission systems are formed of a complex interconnected system of generating plants, substations, and transmission and distribution lines. At a given point in time, a power transmission system may not have perfectly balanced loads, currents, voltages, and impedances in all phases (3 or more). One proposed solution to reducing phase imbalances between the various phases of a power transmission system is to physically transpose (e.g., roll or re-orient) the lines from time-to-time (including for the case where each line is at a different phase).